In an ideal AFM, for every moment pointing in some direction there is another one pointing in the opposite direction. Now consider an AFM in which the 'up' and 'down' moments are organized in crystal planes (e.g. the 111 planes in NiO). If now the surface of the AFM happens to be just such a layer (this would not be natural in NiO, though) than right at the surface (translation symmetry along the surface normal broken!) these moments would not be compensated. this matters because exchange interactions are short ranged.

Thank you Dr.Kai Fauth for sharing the valuable informations.

If in case of thin films of AFM, do this phenomenon of uncompensated moments will in turn create the small remanent net magnetic moments or (the system will compensate for this effect )??

Not necessarily on a meso- or macroscopic scale. Usually there are several equivalent axes along which the moments can align. Typically then, domains form. But locally yes, such tenant magnetization will occur.

The above does NOT say that remnant magnetization of this kind is impossible. When looking up literature on exchange bias then you may well find examples where the magnetization curves are not only displaced on the field axis but also on the magnetization

...axis. This can be an example of this kind. Whether or not this occurs will depend on relative strength of exchange interactin within the AFM and to the FM...

Thank you very much.

HI Saj Mohan, Can you explain compensated and uncompensated moments in AFM in an easily language?